There are nasty versions of this dice game but we'll start with the nice ones...

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Number problems at primary level that may require determination.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you replace the letters with numbers? Is there only one solution in each case?

What is the sum of all the digits in all the integers from one to one million?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

There are six numbers written in five different scripts. Can you sort out which is which?

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

Number problems at primary level to work on with others.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

This activity involves rounding four-digit numbers to the nearest thousand.

Number problems for inquiring primary learners.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Have a go at balancing this equation. Can you find different ways of doing it?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Can you work out some different ways to balance this equation?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

Number problems at primary level that require careful consideration.

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Explore the relationship between simple linear functions and their graphs.

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?